Island Transport

2
5 7
3 3
3 0
3 1
0 0
4 5
1 3 3
2 3 4
2 4 3
1 5 6
4 5 3
1 4 4
3 4 2
6 7
-1 -1
0 1
0 2
1 0
1 1
2 3
1 2 1
2 3 6
4 5 5
5 6 3
1 4 6
2 5 5
3 6 4

9
6

题意：有N个岛屿 M条无向路 每一个路有一最大同意的客流量。求从最西的那个岛屿最多能运用多少乘客到最东的那个岛屿。

题解：最大流，起点为最左的点，终点为最右的点。

#include<algorithm>
#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#define N 100020
#define ll long long

using namespace std;

const int MAXN = 100010;//点数的最大值
const int MAXM = 400010;//边数的最大值
const int INF = 0x3f3f3f3f;

struct Edge {
    int to,next,cap,flow;
} edge[MAXM]; //注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
int n,m;

void init() {
    tol = 0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int w,int rw = 0) {
    edge[tol].to = v;
    edge[tol].cap = w;
    edge[tol].flow = 0;
    edge[tol].next = head[u];
    head[u] = tol++;
    edge[tol].to = u;
    edge[tol].cap = rw;
    edge[tol].flow = 0;
    edge[tol].next = head[v];
    head[v] = tol++;
}

int Q[MAXN];

void BFS(int start,int end) {
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    gap[0] = 1;
    int front = 0, rear = 0;
    dep[end] = 0;
    Q[rear++] = end;
    while(front != rear) {
        int u = Q[front++];
        for(int i = head[u]; i != -1; i = edge[i].next) {
            int v = edge[i].to;
            if(dep[v] != -1)continue;
            Q[rear++] = v;
            dep[v] = dep[u] + 1;
            gap[dep[v]]++;
        }
    }
}
int S[MAXN];

int sap(int start,int end,int n) {
    BFS(start,end);
    memcpy(cur,head,sizeof(head));
    int top = 0;
    int u = start;
    int ans = 0;
    while(dep[start] < n) {
        if(u == end) {
            int Min = INF;
            int inser;
            for(int i = 0; i < top; i++)
                if(Min > edge[S[i]].cap - edge[S[i]].flow) {
                    Min = edge[S[i]].cap - edge[S[i]].flow;
                    inser = i;
                }
            for(int i = 0; i < top; i++) {
                edge[S[i]].flow += Min;
                edge[S[i]^1].flow -= Min;
            }
            ans += Min;
            top = inser;
            u = edge[S[top]^1].to;
            continue;
        }
        bool flag = false;
        int v;
        for(int i = cur[u]; i != -1; i = edge[i].next) {
            v = edge[i].to;
            if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u]) {
                flag = true;
                cur[u] = i;
                break;
            }
        }
        if(flag) {
            S[top++] = cur[u];
            u = v;
            continue;
        }
        int Min = N;
        for(int i = head[u]; i != -1; i = edge[i].next)
            if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min) {
                Min = dep[edge[i].to];
                cur[u] = i;
            }
        gap[dep[u]]--;
        if(!gap[dep[u]])return ans;
        dep[u] = Min + 1;
        gap[dep[u]]++;
        if(u != start)u = edge[S[--top]^1].to;
    }
    return ans;
}

int main() {
    //freopen("test.in","r",stdin);
    int t;
    cin>>t;
    while(t--) {
        scanf("%d%d",&n,&m);
        int s,t;
        int xmin=INF,xmax=-INF;
        int x,y,c;
        for(int i=1; i<=n; i++) {
            scanf("%d%d",&x,&y);
            if(x<xmin) {
                xmin=x;
                s=i;
            }
            if(x>xmax) {
                xmax=x;
                t=i;
            }
        }
        init();
        for(int i=1; i<=m; i++) {
            scanf("%d%d%d",&x,&y,&c);
            addedge(x,y,c,c);
        }
        printf("%d\n",sap(s,t,n));
    }
    return 0;
}